Subject: How many electrons make a semiconductor nanocrystal film metallic

For films of semiconductor nanocrystals to achieve their potential as novel,
low-cost electronic materials, a better understanding of their doping to tune
their conductivity is required. So far, it not known how many dopants will
turn a nanocrystal film from semiconducting to metallic. In bulk
semiconductors, the critical concentration of electrons at the metal-
insulator transition is described by the famous Mott criterion. We show
theoretically that in a dense NC film, where NCs touch each other by small
facets, the concentration of electrons N at the metal-insulator transition
satisfies the condition: N r^3 = 0.3, where r is a radius of contact facets.
In the accompanying experiments, we investigate the conduction mechanism in
films of phosphorus-doped, ligand-free silicon nanocrystals. At the largest
electron concentration achieved in our samples, which is half the predicted
N, we find that the localization length of hopping electrons is close to three
times the nanocrystals diameter, indicating that the film approaches the
metal-insulator transition.